Measurement of spin correlation and entanglement in ATLAS and CMS

This paper presents the latest results from the ATLAS and CMS experiments on precision measurements of top-quark pair spin correlations and quantum entanglement, leveraging extensive proton-proton collision datasets at up to 13.6 TeV to test theoretical predictions through the unique decay properties of top quarks.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. It smashes protons together at nearly the speed of light, creating a chaotic storm of new particles. Among these, the top quark is the "king." It is the heaviest elementary particle in our universe, about as heavy as a gold atom but packed into a space smaller than an atom.

Because it is so heavy, it interacts strongly with the Higgs boson (the particle that gives things mass). But here is the most interesting part: the top quark is incredibly short-lived. It dies so fast (in a trillionth of a trillionth of a second) that it doesn't have time to "dress up" or get tangled up with other particles to form normal matter (a process called hadronization).

The "Naked" Quark
Think of most particles like a shy person who puts on a coat and hat before leaving the house. They hide their true self. The top quark is different; it's like a person who runs out the door so fast they are still in their pajamas. Because it dies before it can "dress up," it carries its spin (a quantum property like a tiny internal compass) directly into its decay products.

This allows scientists at the ATLAS and CMS detectors to look at the "pajamas" (the particles the top quark turns into) and figure out exactly which way the top quark's internal compass was pointing.

The Main Story: Are They Entangled?

The paper discusses two main experiments: ATLAS and CMS. They are like two giant, high-tech cameras taking millions of photos of these top quark collisions.

1. The "Dance Partner" Analogy (Spin Correlation)
Imagine two dancers spinning on a floor. In classical physics, if you push one, the other might move, but they are independent. In quantum physics, however, these two top quarks are like entangled dance partners. Even though they are flying apart at high speeds, their spins are linked. If one spins "up," the other is statistically likely to spin "down" in a specific way.

The scientists measured the angles of the particles the top quarks decayed into. It's like watching the footprints left behind by the dancers to figure out how they were spinning while they were dancing.

• The Result: Both ATLAS and CMS confirmed that these "dance partners" are indeed spinning in a correlated way, exactly as predicted by our current laws of physics (the Standard Model).

2. The "Spooky Connection" (Quantum Entanglement)
This is the big breakthrough. Quantum entanglement is what Einstein famously called "spooky action at a distance." It means two particles are so deeply connected that measuring one instantly tells you the state of the other, no matter how far apart they are.

Usually, we see this with tiny things like photons (light particles) in a quiet lab. But this paper reports the first time we have seen this "spooky connection" in the heavy, high-energy world of top quarks.

• The Threshold Zone: The scientists focused on a specific "slow-motion" zone where the top quarks are created with just enough energy to exist (the threshold). In this zone, the two quarks are most likely to be in a "singlet" state—a perfect quantum handshake where their spins cancel each other out.
• The Discovery: By analyzing the data, ATLAS and CMS found that in this specific zone, the top quarks are definitely entangled. The statistical evidence is so strong (more than 5 "sigma," which is like flipping a coin and getting heads 50 times in a row by pure luck) that we can say with near certainty: Yes, heavy top quarks can be quantumly entangled.

The Challenges and Surprises

The "Blind Spot" Problem
In one of the decay channels (where one top quark turns into jets of particles), it's very hard to tell which specific particle came from the "down-type" quark. It's like trying to find a specific red sock in a pile of laundry where all the socks look similar.

• The Solution: The CMS team used a super-smart computer program (an Artificial Neural Network) to act like a detective, analyzing the "texture" of the jets to identify the right particle. This allowed them to measure spin correlations in a new way.

The "Glitch" in the Matrix
While the experiments confirmed that entanglement exists, there is a small mystery. In the "threshold" region (where the quarks are created just barely), the data doesn't perfectly match the theoretical predictions. The "dance" seems slightly more intense than the math says it should be.

• The Theory: Scientists think this might be because the top quarks are forming a temporary, ghostly "quasi-bound state" (like a brief, fuzzy hug before they fly apart) that our current computer models don't fully capture yet. This is an exciting puzzle for theorists to solve.

Why Does This Matter?

You might ask, "Why do we care if heavy particles are entangled?"

1. Testing Reality: It proves that quantum mechanics (the rules of the very small) works even at the highest energies and with the heaviest particles we know. It bridges the gap between the quantum world and the high-energy world of particle colliders.
2. Future Tech: Understanding how to manipulate and measure these quantum states in high-energy collisions could be a stepping stone for future quantum technologies.
3. New Physics: The slight mismatches between the data and the theory might be the first hint of "New Physics"—something beyond our current understanding of the universe.

Summary

In simple terms, the ATLAS and CMS teams have taken the world's most powerful microscope, looked at the heaviest particles in the universe, and confirmed that even the heaviest, fastest particles can share a "spooky" quantum connection. They have successfully measured how these particles spin together and proved that quantum entanglement isn't just a lab trick for light particles; it's a fundamental part of the high-energy universe.

Technical Summary

1. Problem and Motivation

The top quark, with a mass of $\approx 172.7$ GeV, is the heaviest elementary particle in the Standard Model (SM). Its unique property of decaying before hadronization ($\tau \sim 10^{-25}$ s vs. hadronization time $\sim 10^{-23}$ s) allows its spin information to be transferred directly to its decay products. This makes the top quark an ideal system for probing quantum mechanical phenomena at the TeV energy scale, specifically spin correlations and quantum entanglement.

While quantum mechanics (QM) has been tested extensively at low energies using photons and ions, high-energy proton-proton ($pp$) collisions at the Large Hadron Collider (LHC) offer a novel regime to investigate quantum effects in the quark sector. The paper addresses the challenge of reconstructing the $t\bar{t}$ quantum state (described by a density matrix $\rho$) and testing the SM prediction that top-quark pairs are entangled, particularly near the production threshold and in high-energy boosted regimes.

2. Methodology

The analysis relies on the fact that the spin density matrix of a $t\bar{t}$ pair can be reconstructed from the angular distributions of decay products.

• Theoretical Framework:

  • The $t\bar{t}$ system is treated as a bipartite quantum system (two qubits).
  • The state is described by a density matrix $\rho$ expanded in the basis of Pauli matrices ($\sigma_i$).
  • The differential cross-section depends on spin analyzing powers ($\alpha$) and the spin correlation matrix ($C_{ij}$).
  • Entanglement Criterion: The Peres-Horodecki criterion is used. A state is entangled if the partial transpose of the density matrix has negative eigenvalues. For $t\bar{t}$, this translates to specific kinematic conditions:
    • Threshold Region: Entanglement is expected if the trace of the correlation matrix satisfies $\text{tr}[C] + 1 < 0$. This is quantified by the witness $D = \text{tr}[C]/3$, where entanglement implies $D < -1/3$.
    • Boosted Region: A modified witness $\tilde{D}$ or a matrix-based observable $\Delta E = C_{nn} + |C_{rr} + C_{kk}|$ is used, where $\Delta E > 1$ signals entanglement.

• Experimental Channels:

  • Dilepton Channel ($e^+e^-, e^\pm\mu^\mp, \mu^+\mu^-$): Both top quarks decay semi-leptonically. Charged leptons are ideal spin analyzers ($|\alpha| \approx 1$). Used by both ATLAS and CMS for threshold measurements.
  • Lepton+Jets Channel: One top decays hadronically. Identifying the down-type quark jet from the $W$ boson decay is challenging. CMS employs an Artificial Neural Network (ANN) utilizing heavy-flavor tagging algorithms to identify $c$-jets and infer the down-type jet.

• Data Sets:

  • CMS: 2016 data ($\sqrt{s}=13$ TeV, $36.3$ fb$^{-1}$) for threshold; Full Run 2 data ($138$ fb$^{-1}$) for inclusive and boosted measurements.
  • ATLAS: 2015–2016 data ($\sqrt{s}=13$ TeV, $36.1$ fb$^{-1}$) for spin correlations; 2015–2018 data ($140$ fb$^{-1}$) for the first entanglement observation.

• Analysis Techniques:

  • Unfolding: Measured angular distributions are unfolded to the parton level using regularized methods (TUnfold for CMS, iterative Bayesian for ATLAS) to correct for detector resolution and acceptance.
  • Fitting: Binned maximum-likelihood fits are performed on observables like $\Delta\phi(l^+, l^-)$ or $\cos\phi$ to extract spin coefficients ($C_{ij}$) and entanglement witnesses.
  • Modeling: Comparisons are made against SM predictions using Monte Carlo generators (POWHEG, MADGRAPH5_aMC@NLO, MG5_aMC@NLO) interfaced with parton showers (PYTHIA8, HERWIG7). CMS incorporates a simplified model for $t\bar{t}$ quasi-bound states ($\eta_t$ resonance) in the threshold region.

3. Key Contributions and Results

A. Spin Correlations and Polarization

• Full Density Matrix Reconstruction: Both collaborations successfully extracted all 15 coefficients of the $t\bar{t}$ spin-density matrix.
• CMS Results: Measured coefficients in the dilepton channel agree with SM expectations. The fraction of SM-like spin correlation ($f_{SM}$) is consistent with unity.
• ATLAS Results: Measured $f_{SM}$ in bins of invariant mass ($m_{t\bar{t}}$). The inclusive measurement shows a slight excess over the SM prediction ($f_{SM} \approx 1.25$), corresponding to a deviation of $\approx 2.2\sigma$.

B. First Observation of Quantum Entanglement (Threshold Region)

• ATLAS: Performed the first measurement of entanglement at the LHC in the threshold region ($340 < m_{t\bar{t}} < 380$ GeV).
  • Measured witness: $D = -0.537 \pm 0.002(\text{stat}) \pm 0.019(\text{syst})$.
  • Result: The value is significantly below the separability bound ($D < -1/3$), confirming entanglement with a significance exceeding 5$\sigma$.
  • Tension: A discrepancy exists between data and SM predictions (specifically parton-shower modeling) in this region, suggesting current models may not fully capture threshold dynamics.
• CMS: Confirmed entanglement in the threshold region ($345 < m_{t\bar{t}} < 400$ GeV) with >5$\sigma$ significance.
  • Novelty: This analysis included, for the first time at the LHC, a simplified model of $t\bar{t}$ quasi-bound states ($\eta_t$). The data is better described when this resonance is included, though the effect is primarily driven by normalization.

C. Entanglement in the Boosted Regime

• CMS: Extended the search to the high-mass, boosted regime ($m_{t\bar{t}} > 800$ GeV).
  • Used the observable $\Delta E$ derived from the full spin-density matrix.
  • Result: Entanglement was observed with a significance of 6.7$\sigma$ (observed) / 5.6$\sigma$ (expected) relative to separable states. This demonstrates that quantum entanglement persists even at high energies and large scattering angles.

D. Lepton+Jets Channel

• CMS: Successfully applied spin analysis to the lepton+jets channel using the full Run 2 dataset.
  • Developed an ANN to identify the down-type quark jet, overcoming the challenge of jet flavor assignment.
  • Results for the full spin-density matrix and entanglement witness $\Delta E$ are consistent with SM predictions.

4. Significance

• Validation of QM at High Energy: These results provide the first direct experimental evidence that quantum entanglement, a phenomenon typically associated with low-energy systems, persists in high-energy particle collisions involving heavy quarks.
• Precision Tests of the SM: The measurements serve as stringent tests of the Standard Model. While the observation of entanglement confirms SM predictions, the observed tension in the threshold region (between data and current MC models) highlights gaps in our theoretical understanding of $t\bar{t}$ production dynamics, particularly regarding quasi-bound states and parton shower modeling.
• New Physics Portal: The ability to reconstruct the full quantum state of the top quark opens a new frontier for "Quantum Information" studies in particle physics. It paves the way for future tests of Bell inequalities and the study of other quantum properties like "Magic" (quantified computational advantage), which CMS has also begun to measure.
• Methodological Advancement: The successful application of machine learning (ANNs) for jet identification and the development of entanglement witnesses for both threshold and boosted regimes establish robust methodologies for future high-precision quantum measurements at the LHC.

In conclusion, the ATLAS and CMS collaborations have successfully transitioned top-quark physics from classical kinematic measurements to the realm of quantum information science, confirming the entangled nature of top-quark pairs and setting the stage for deeper investigations into the quantum dynamics of the Standard Model.